Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(x^{-\left(\frac{3}{2}\right)}\right)$ using the power rule

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Final Answer

$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$

Choose the solving method

1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$-\frac{3}{2}x^{-\frac{5}{2}}$
2

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$

Final Answer

$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$
$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$

Main topic:

Power rule

Related formulas:

1. See formulas

Time to solve it:

~ 0.03 s (SnapXam)